The assessment of model fit in latent trait modeling is an integral part of correctly applying the model. Still the assessment of model fit has been less utilized for ideal point models such as the Generalized Graded Unfolding Models (GGUM). The current study assesses the performance of the relative fit indices "AIC" and "BIC," and the absolute fit adjusted chi-square statistic for the GGUM for both dichotomous and polytomous data. Factors included data generation model, sample size, instrument length, and screening value. Results show that relative fit indices performed well in identifying the GGUM when at least 20-items were used. For polytomous data the correct generation model was identified as the best fitting mode irrespective of the number of items and sample size. The adjusted chi-square statistic performed well in correctly identifying GGUM as the best fit for the GGUM dichotomous data generation, but performed poorly with the dominance models. With polytomous data case these fit indices always correctly identified GGUM as the best fit for the GGUM data. An explanation for this performance is provided.